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A key problem in high-resolution multidimensional parameter estimation via unitary ESPRIT is to jointly solve a set of invariance equations by means of least-squares minimization. It has been shown previously that existing least-squares techniques fail when applied to the category of cross arrays, which consist of perpendicular uniform linear arrays crossing at the center of the array. Cross array geometries are of special interest because they provide a larger aperture and, hence, better resolution for a given number of array elements than other multidimensional uniform array geometries. This letter proposes an improved structured least-squares method that enables successful application of unitary ESPRIT to cross arrays. Results of simulated direction-of-arrival estimation experiments using a three-dimensional cross array indicate that considerable performance improvements can be achieved if the new method is used.